I suspect that your AND function might be a problem - AND only returns a single result not an array of results as required, try using multiple IFs like this
=min(if(car_number = indirect("number_vector"),IF(indirect(data_vector)<>0, indirect(data_vector))))
Note that I also used <> rather than using NOT
Are data vector and number vector the same size and shape? (both vertical?) why are there quotes around one but not the other?